Answer:
Step-by-step explanation:
1. Equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
If (h, k) is (2, 8) and r = 10:
(x - 2)² + (y - 8)² = 100
2. The vertex and focus have the same x-coordinate, so this is a vertical parabola. Equation of a vertical parabola is:
y = 1/(4p) (x - h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
If (h, k) is (2, 2) and p = 5-2 = 3:
y = 1/12 (x - 2)² + 2
3. The directrix is a vertical line, so this is a horizontal parabola. Equation of a horizontal parabola is:
x = 1/(4p) (y - k)² + h
The distance between the directrix and the vertex is the same as p.
If (h, k) is (5, 2) and p = 5-3 = 2:
x = 1/8 (y - 2)² + 5
